Simple algebraic technique for nearly orthogonal grid generation

Abstract

RID generation is a very important aspect of solving computational fluid dynamics (CFD) problems where a set of partial differential equations has to be solved in a given domain. It is desirable for the grid to have good orthogonality properties, and the grid generator should be able to produce an arbitrary amount of clustering near the body surface when necessary. Generation of body-fitted coordinates meeting these requirements using algebraic techniques are described by Eiseman1 and Smith.2 It is well known that the most efficient way of dividing the domain for external flow problems is by generating an O-type grid for a twodimensional case or an O-O topology grid for a three-dimensional case, since they give the maximum resolution near the body surface with the minimum number of grid points. A simple algebraic technique has been developed for generating an O-type grid or an O-O topology grid for a geometry with sharp edges having a high grid density near the body surface while maintaining orthogonality. The present method generates the grid by distributing spacings in the outward normal direction from a closed contour as a function of the rate of change of arc length in that direction. This procedure, when applied to subsequently generated contours, evolves a nearly orthogonal grid with a circular outer boundary. A similar procedure applied to a closed three-dimensional surface produces a spherical outer boundary, thereby generating an O-O topology grid.